
From:  Kostas Oikonomou 
Subject:  [Axiomdeveloper] Re: [Axiommail] beginner question about sum(...) 
Date:  Tue, 01 Feb 2005 09:01:44 0500 
Useragent:  Opera M2/7.54 (SunOS, build 751) 
Hello Martin, I was thinking about this a bit more. If "a" is a positive integer, of course the sum 1/(k*(k+a)) is hypergeometric. And indeed Axiom evaluates it if you give "a" a positive integral value. Now wouldn't you expect that if you declared "a" to be a positive integer the summation would be evaluated? It is not. Instead Axiom says that "a" has not been given a value. A short while ago, Bill Page also posted a message about this general situation. That if you make a certain type declaration, you would expect Axiom to act accordingly, but it does not appear to do so. Regards, Kostas
Dear Kostas, Kostas Oikonomou writes: > > But I was disappointed by the sum(1/k^2, k=1..n) example. I saw that > Gosper's method is implemented in sum.spad.pamphlet, but this (rather > simple) sum needs symbolic manipulation of gamma and psi functions, which is > not there. More generally, special functions seem to be handled only > numerically. At least for my prospective use of Axiom, this points to a > rather big "hole". And I wonder how many others of this sort there are. > > I also tried sum(1/(k*(k+a)), k=1..n). That was also returned unevaluated, > although Gosper's method should handle it. Why should Gosper's method handle it? As far as I can see the solution is not hypergeometric? Martin
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